## Algebra and Trigonometry 10th Edition

$$\frac{x^{2}}{2(x+4)}$$
The area of the smaller triangle A = $\frac{x(x+2)}{2}$ The area of the bigger triangle B = $\frac{(x+2)(x+4)}{x}$ The area of the shaded area = $B-A$ The area of the non-shaded area = $A$ The ratio between non-shaded area to shaded area = $\frac{A}{B-A}$=$\frac{\frac{x(x+2)}{2}}{\frac{(x+2)(x+4)}{x}}$= $\frac{\frac{x}{2}}{\frac{x+4}{x}}$=$\frac{x^{2}}{2(x+4)}$ (simplifying the complex fraction)